solve a system with matrix inverses or augmented matrices

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ren writes the system x + 2y − z = 4, 3x − y = 5, and 2y + z = 1 as AX = B. Which matrix equation is it?

   • [1, 3, 0; 2, -1, 2; -1, 0, 1][x; y; z] = [4; 5; 1]
   • [1, 2, -1; 3, -1, 0; 2, 1, 0][x; y; z] = [4; 5; 1]
   • [1, 2, -1; 3, -1, 0; 0, 2, 1][4; 5; 1] = [x; y; z]
   • [1, 2, -1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]
   • [1, 2, 1; 3, -1, 0; 0, 2, 1][x; y; z] = [4; 5; 1]
2. 2.

   Tala writes the system 2x − y + z = 3, x + 4z = 2, and y − 3z = 6 as AX = B. Which matrix equation is it?

   • [2, -1, 1; 1, 0, 4; 0, 1, -3][3; 2; 6] = [x; y; z]
   • [2, 1, 0; -1, 0, 1; 1, 4, -3][x; y; z] = [3; 2; 6]
   • [2, -1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
   • [2, 1, 1; 1, 0, 4; 0, 1, -3][x; y; z] = [3; 2; 6]
   • [2, -1, 1; 1, 4, 0; 0, 1, -3][x; y; z] = [3; 2; 6]
3. 3.

   Zee writes the system 3y + 2x = 8 and x − 4y = 1 as AX = B. Which matrix equation is it?

   • [2, 3; 1, -4][8; 1] = [x; y]
   • [2, 3; 1, 4][x; y] = [8; 1]
   • [2, 3; 1, -4][x; y] = [8; 1]
   • [2, 1; 3, -4][x; y] = [8; 1]
   • [3, 2; 1, -4][x; y] = [8; 1]
4. 4.

   5x + 2y = -7; 7x + 3y = -9. Number table A = [5, 2; 7, 3]. Noah solves the system in the figure with X = A⁻¹B, where A⁻¹ = [3, -2; -7, 5] and B = [-7; -9]. What is y?

   4
5. 5.

   3x + 5y = 13; x + 4y = 2. Number table A = [3, 5; 1, 4]. Pia solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/7)[4, -5; -1, 3] and B = [13; 2]. What is x?

   6
6. 6.

   Esme replaces row 2 of [1, 3 | 7; 4, 5 | 6] with row 2 − 4 × row 1. What is the new number in row 2, after the bar?

   -22
7. 7.

   Jun replaces row 2 of [2, -1 | 5; 6, 4 | 3] with row 2 − 3 × row 1. What is the new number in row 2, in column 2?

   7
8. 8.

   Tala solves 4x + y = 5 and 3x + 2y = 0 with X = A⁻¹B. What is y?

   -3

9. Read this first

   Start

   [1, 2, -1 | 7; 2, 5, 1 | 24; 1, 5, 9 | 39]. Row steps: row 2 − 2 × row 1, then row 3 − row 1, then row 3 − 3 × row 2.

10. 9.

    Tala row-reduces the system in the figure to the last table [1, 2, -1 | 7; 0, 1, 3 | 10; 0, 0, 1 | 2]. What is y?

    4

11. Start

    [1, 3, 2 | 11; 2, 7, 2 | 15; 5, 16, 9 | 51]. Row steps: row 2 − 2 × row 1, then row 3 − 5 × row 1, then row 3 − row 2.

12. 10.

    Bo row-reduces the system in the figure to the last table [1, 3, 2 | 11; 0, 1, -2 | -7; 0, 0, 1 | 3]. What is x?

    8